Constraining slow-roll inflation in the presence of dynamical dark energy

In this Letter we perform a global analysis of the constraints on the inflationary parameters in the presence of dynamical dark energy models from the current observations, including the three-year Wilkinson Microwave Anisotropy Probe (WMAP3) data, Boomerang-2K2, CBI, VSA, ACBAR, SDSS LRG, 2dFGRS and ESSENCE (192 sample). We use the analytic description of the inflationary power spectra in terms of the horizon-flow parameters {epsilon(i)} With the first order approximation in the slow-roll expansion, we find that the constraints on the horizon-flow parameters are epsilon(1) < 0.014 (95% C.L.) and epsilon(2) =0.034 +/- 0.024 (1 sigma) in the ACDM model. In the framework of dynamical dark energy models, the constraints become obviously weak, epsilon(1) < 0.022 (95% C.L.) and epsilon(2) = -0.006 +/- 0.039 (1 sigma), and the inflation models with a "blue" tilt, which are excluded about 2 sigma in the ACDM model, are allowed now. With the second order approximation, the constraints on the horizon-flow parameters are significantly relaxed further. If considering the non-zero epsilon(3), the large running of the scalar spectral index is found for the ACDM model, as well as the dynamical dark energy models. (C) 2008 Elsevier B.V. All rights reserved.